Finite Group Databasebeta

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C121×D117 #43246830

order28314
automorphism?
homologyAbelianization (H1) = C2×C121 · Schur multiplier (H2) = C1

Aliases

direct productC121×D117
unambiguous semidirect productC9⋊(D13×C121)
unambiguous semidirect productC13⋊(D9×C121)

Splittings

Fitting, HallC9×C13×C121 ⋊ C2
derived, HallC9×C13 ⋊ C2×C121
HallC13×C121 ⋊ D9
HallC9×C121 ⋊ D13
SylowC13 ⋊ D9×C121
SylowC9 ⋊ D13×C121

Subgroups

subgroupG/H
center, hypercenterC121D117
commutator, hypocenterC9×C13C2×C121
FrattiniC3×C11C11×D39
FittingC9×C13×C121C2
socleC3×C11×C13D3×C11
prime radicalC11×D117C11
cosocleC9×C11×C13C2×C11
LCSG ▷ C9×C13
UCSC1 ◁ C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14157

Conjugacy classes & character table

7260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28314, 10);